I found my answer and wanted to post a detailed response as only found limited reference to this. I opened up both of the handsets, and there was a little tab that had broken off of the steering wheels that connected the wheel to the mechanism that caused the wheels to turn. I was able to pop the broken tab out of the mechanism and glue it back in place on the steering wheel, then after letting it dry, reconnecting the setup. So far, it works again, though I'm suspicious that with some hard play, it will happen again sometime.
Someone in another posting made reference to wanting to come up with a mod to the handset that is more secure. If anyone does that, I'd love to hear about it.
Hope that helps someone along the way.